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I was learning about the physics behind "mirascopes" from a number of online resources. It's explained that a mirascope consist of two concave parabolic mirrors of equal focal length placed on top of each other in such a way their principal axes coincide. Further the distance between the poles of the two mirrors is exactly equal to the focal lengths of the two mirrors.

Let us consider the following diagram:

enter image description here

An object placed on the bottom mirror will be at the focal plane of the mirror at the top. Hence, rays emerging from the object will get reflected parallel to the principal axis after the reflection from the upper mirror. These rays being parallel to the principal axis get focussed at the focal plane of the mirror at the bottom after second reflection. Thus a real inverted image is formed near the hole.

On the lines of my understanding, either parabolic or spherical concave mirrors could be used since their functionality is almost same for an object placed at their focal points. However, according to the sources I referred, only parabolic mirrors are used to make mirascopes. So, what happens if we use a spherical concave mirror instead of a parabolic mirror? What will be the effects on the image formed?

My thoughts:

I think a parabolic mirror is a better option over concave mirror, as the spherical aberration in the former is comparatively lesser than the latter one. I inferred this point from the following text from a Wikipedia article:

Spherical mirrors, however, suffer from spherical aberration — parallel rays reflected from such mirrors do not focus to a single point. For parallel rays, such as those coming from a very distant object, a parabolic reflector can do a better job.

But I'm not sure whether this is the reason why parabolic mirrors are used in mirascopes as I think for a object which doesn't produce it's own light, it's illuminated only because of light coming from the hole on the upper mirror and hence marginal rays (rays far away from principal axis) are not of great importance.

References:

  1. University of Wisconsin-Madison
  2. The Mirascope: an explanation on a conceptual level

Image Courtesy : My own work :)

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(Note: this answer addresses v1 or v3. The question has since been revised.)

I think the miraskope - at least two different I own- are spherical. They are very cheap , about 5 and 10$ so the manufacturing is cheap, they function well since they make only pictures of relatively small objects , but I suppose in big science Museums parabolas are used to show larger 3d objects

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(Note: this answer addresses v1 or v3. The question has since been revised.)

It looks like you are having some minor confusion over vocabulary. Mirrors can be flat or concave or convex. In this case we are talking about concave mirrors.

Concave mirrors can be shaped like a sphere or a parabola or something else. A parabola is better because it is the perfect shape to reflect rays that come from a point into parallel rays. A telescope does the reverse. It takes parallel rays from distant stars and reflects them to a point. A parabola does this too.

But spheres are much easier to make when grinding a lens or mirror. The curvature is the same everywhere. So many telescopes use spherical mirrors.

For telescopes, mirrors have gentle curves, not that far from flat. In this case, the difference between a spherical and parabolic mirror is small, often just a few wavelengths of light. In this case, a spherical mirror does a pretty good job.

A mirascope is more strongly curved than a typical telescope mirror. A parabolic mirror would be better in this case.

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  • $\begingroup$ Thank you for your answer :) I understood parabolic mirrors could be concave or convex. Here, I think the "concave mirror" refers to a spherical mirror rather than a parabolic. I've slightly modified my question as "Which type of mirror does a mirascope use - spherical or parabolic?" So to the new question - the answer is mostly parabolic and the reason for that is minimizing spherical aberration. Am I right? $\endgroup$ – Guru Vishnu Jan 27 at 2:56
  • $\begingroup$ BTW, according to "It looks like you are having some minor confusion over vocabulary. Mirrors can be flat or concave or convex. In this case we are talking about concave mirrors.": I'm not confused because of terminologies. It's because I've used the term "concave mirrors" predominantly for spherical mirrors. If the websites meant a parabolic mirror instead of spherical concave mirror, I wouldn't have asked this question if they referred to them as "concave parabolic mirrors" :) $\endgroup$ – Guru Vishnu Jan 27 at 2:59
  • $\begingroup$ Hi. I've made some changes to my question. If you could address all the issues, and make changes accordingly, I'll proceed towards acceptance of your answer. Thanks! $\endgroup$ – Guru Vishnu Jan 27 at 11:33

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